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<li><a class="reference internal" href="#">Comparing anomaly detection algorithms for outlier detection on toy datasets</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-plot-anomaly-comparison-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="comparing-anomaly-detection-algorithms-for-outlier-detection-on-toy-datasets">
<span id="sphx-glr-auto-examples-plot-anomaly-comparison-py"></span><h1>Comparing anomaly detection algorithms for outlier detection on toy datasets<a class="headerlink" href="#comparing-anomaly-detection-algorithms-for-outlier-detection-on-toy-datasets" title="Permalink to this headline">¶</a></h1>
<p>This example shows characteristics of different anomaly detection algorithms
on 2D datasets. Datasets contain one or two modes (regions of high density)
to illustrate the ability of algorithms to cope with multimodal data.</p>
<p>For each dataset, 15% of samples are generated as random uniform noise. This
proportion is the value given to the nu parameter of the OneClassSVM and the
contamination parameter of the other outlier detection algorithms.
Decision boundaries between inliers and outliers are displayed in black
except for Local Outlier Factor (LOF) as it has no predict method to be applied
on new data when it is used for outlier detection.</p>
<p>The <a class="reference internal" href="../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.svm.OneClassSVM</span></code></a> is known to be sensitive to outliers and
thus does not perform very well for outlier detection. This estimator is best
suited for novelty detection when the training set is not contaminated by
outliers. That said, outlier detection in high-dimension, or without any
assumptions on the distribution of the inlying data is very challenging, and a
One-class SVM might give useful results in these situations depending on the
value of its hyperparameters.</p>
<p><a class="reference internal" href="../modules/generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.covariance.EllipticEnvelope</span></code></a> assumes the data is Gaussian and
learns an ellipse. It thus degrades when the data is not unimodal. Notice
however that this estimator is robust to outliers.</p>
<p><a class="reference internal" href="../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.ensemble.IsolationForest</span></code></a> and
<a class="reference internal" href="../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.neighbors.LocalOutlierFactor</span></code></a> seem to perform reasonably well
for multi-modal data sets. The advantage of
<a class="reference internal" href="../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.neighbors.LocalOutlierFactor</span></code></a> over the other estimators is
shown for the third data set, where the two modes have different densities.
This advantage is explained by the local aspect of LOF, meaning that it only
compares the score of abnormality of one sample with the scores of its
neighbors.</p>
<p>Finally, for the last data set, it is hard to say that one sample is more
abnormal than another sample as they are uniformly distributed in a
hypercube. Except for the <a class="reference internal" href="../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.svm.OneClassSVM</span></code></a> which overfits a
little, all estimators present decent solutions for this situation. In such a
case, it would be wise to look more closely at the scores of abnormality of
the samples as a good estimator should assign similar scores to all the
samples.</p>
<p>While these examples give some intuition about the algorithms, this
intuition might not apply to very high dimensional data.</p>
<p>Finally, note that parameters of the models have been here handpicked but
that in practice they need to be adjusted. In the absence of labelled data,
the problem is completely unsupervised so model selection can be a challenge.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Alexandre Gramfort &lt;alexandre.gramfort@inria.fr&gt;</span>
<span class="c1">#         Albert Thomas &lt;albert.thomas@telecom-paristech.fr&gt;</span>
<span class="c1"># License: BSD 3 clause</span>

<span class="kn">import</span> <span class="nn">time</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_moons</span><span class="p">,</span> <span class="n">make_blobs</span>
<span class="kn">from</span> <span class="nn">sklearn.covariance</span> <span class="kn">import</span> <span class="n">EllipticEnvelope</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">IsolationForest</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">LocalOutlierFactor</span>

<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;contour.negative_linestyle&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;solid&#39;</span>

<span class="c1"># Example settings</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">300</span>
<span class="n">outliers_fraction</span> <span class="o">=</span> <span class="mf">0.15</span>
<span class="n">n_outliers</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">outliers_fraction</span> <span class="o">*</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">n_inliers</span> <span class="o">=</span> <span class="n">n_samples</span> <span class="o">-</span> <span class="n">n_outliers</span>

<span class="c1"># define outlier/anomaly detection methods to be compared</span>
<span class="n">anomaly_algorithms</span> <span class="o">=</span> <span class="p">[</span>
    <span class="p">(</span><span class="s2">&quot;Robust covariance&quot;</span><span class="p">,</span> <span class="n">EllipticEnvelope</span><span class="p">(</span><span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">)),</span>
    <span class="p">(</span><span class="s2">&quot;One-Class SVM&quot;</span><span class="p">,</span> <span class="n">svm</span><span class="o">.</span><span class="n">OneClassSVM</span><span class="p">(</span><span class="n">nu</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s2">&quot;rbf&quot;</span><span class="p">,</span>
                                      <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)),</span>
    <span class="p">(</span><span class="s2">&quot;Isolation Forest&quot;</span><span class="p">,</span> <span class="n">IsolationForest</span><span class="p">(</span><span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">,</span>
                                         <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)),</span>
    <span class="p">(</span><span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">,</span> <span class="n">LocalOutlierFactor</span><span class="p">(</span>
        <span class="n">n_neighbors</span><span class="o">=</span><span class="mi">35</span><span class="p">,</span> <span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">))]</span>

<span class="c1"># Define datasets</span>
<span class="n">blobs_params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">n_samples</span><span class="o">=</span><span class="n">n_inliers</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">datasets</span> <span class="o">=</span> <span class="p">[</span>
    <span class="n">make_blobs</span><span class="p">(</span><span class="n">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
               <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span>
    <span class="n">make_blobs</span><span class="p">(</span><span class="n">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span>
               <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span>
    <span class="n">make_blobs</span><span class="p">(</span><span class="n">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="p">[</span><span class="mf">1.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">3</span><span class="p">],</span>
               <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span>
    <span class="mf">4.</span> <span class="o">*</span> <span class="p">(</span><span class="n">make_moons</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">noise</span><span class="o">=.</span><span class="mi">05</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span>
          <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">])),</span>
    <span class="mf">14.</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">)]</span>

<span class="c1"># Compare given classifiers under given settings</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">150</span><span class="p">),</span>
                     <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">150</span><span class="p">))</span>

<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">anomaly_algorithms</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">3</span><span class="p">,</span> <span class="mf">12.5</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">left</span><span class="o">=.</span><span class="mi">02</span><span class="p">,</span> <span class="n">right</span><span class="o">=.</span><span class="mi">98</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=.</span><span class="mi">001</span><span class="p">,</span> <span class="n">top</span><span class="o">=.</span><span class="mi">96</span><span class="p">,</span> <span class="n">wspace</span><span class="o">=.</span><span class="mi">05</span><span class="p">,</span>
                    <span class="n">hspace</span><span class="o">=.</span><span class="mi">01</span><span class="p">)</span>

<span class="n">plot_num</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>

<span class="k">for</span> <span class="n">i_dataset</span><span class="p">,</span> <span class="n">X</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">datasets</span><span class="p">):</span>
    <span class="c1"># Add outliers</span>
    <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=-</span><span class="mi">6</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span>
                       <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">n_outliers</span><span class="p">,</span> <span class="mi">2</span><span class="p">))],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

    <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">algorithm</span> <span class="ow">in</span> <span class="n">anomaly_algorithms</span><span class="p">:</span>
        <span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
        <span class="n">algorithm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
        <span class="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">datasets</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">anomaly_algorithms</span><span class="p">),</span> <span class="n">plot_num</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">i_dataset</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">18</span><span class="p">)</span>

        <span class="c1"># fit the data and tag outliers</span>
        <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">:</span>
            <span class="n">y_pred</span> <span class="o">=</span> <span class="n">algorithm</span><span class="o">.</span><span class="n">fit_predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">y_pred</span> <span class="o">=</span> <span class="n">algorithm</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>

        <span class="c1"># plot the levels lines and the points</span>
        <span class="k">if</span> <span class="n">name</span> <span class="o">!=</span> <span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">:</span>  <span class="c1"># LOF does not implement predict</span>
            <span class="n">Z</span> <span class="o">=</span> <span class="n">algorithm</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
            <span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
            <span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">linewidths</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">)</span>

        <span class="n">colors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="s1">&#39;#377eb8&#39;</span><span class="p">,</span> <span class="s1">&#39;#ff7f00&#39;</span><span class="p">])</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">colors</span><span class="p">[(</span><span class="n">y_pred</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">])</span>

        <span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">(())</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">yticks</span><span class="p">(())</span>
        <span class="n">plt</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="o">.</span><span class="mi">99</span><span class="p">,</span> <span class="o">.</span><span class="mi">01</span><span class="p">,</span> <span class="p">(</span><span class="s1">&#39;</span><span class="si">%.2f</span><span class="s1">s&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">),</span>
                 <span class="n">transform</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">transAxes</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span>
                 <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">&#39;right&#39;</span><span class="p">)</span>
        <span class="n">plot_num</span> <span class="o">+=</span> <span class="mi">1</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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